Finite Group Databasebeta

← #14658441

Subgroups — #14658441

Order 2816.

306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069604C211yesmaximal, characteristic
2#13069392C211yesmaximal, characteristic
3#13067369C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#1570C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66883—21no—
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C4×#4318C2211yescharacteristic
16C11×#334—22no—
17#10622192—21no—
18#10622192—21no—
19#10622190—21no—
20#10622119—22no—
21#10622119—21no—
22#10622119—21no—
23#10622118—21no—
24#10622117—21no—
25C22×Dic22Q812yes—
26C2×C11×M16—21no—
27C22×C8×C11—21no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×#4318—21no—
32C2×#4318D411yescharacteristic
33C2×#4318D411yescharacteristic
34C22×C11⋊C8—21no—
35#66922—21no—
36#66922—21no—
37#66922—21no—
38#66922—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C11×C4⋊C8D411yescharacteristic
44C11×C4⋊C8D412yes—
45C11×C22⋊C8—21no—
46C4×C8×C11—21no—
47#66883—42no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52#66867—21no—
53C4×C11⋊C8—21no—
54#10609—111nomaximal, Sylow
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×Q811yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×Dic11—22no—
59C2×Dic22—22no—
60C2×Dic22—22no—
61C2×Dic22—82no—
62C11×M16—41no—
63C11×M16—41no—
64C2×C8×C11—21no—
65C2×C8×C11—21no—
66C2×C8×C11—22no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C42×C11C2×D411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11#4111yescharacteristic
73C42×C11#4111yescharacteristic
74C4⋊Dic11—41no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78#4318—21no—
79#4318—21no—
80#4318—21no—
81#4318—41no—
82#4318—41no—
83#4318SD1612yes—
84C2×C11⋊C8—21no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—81no—
89#1997—111no—
90#1950—111no—
91#1570D1111yescharacteristic
92#1565—111no—
93#1548—111no—
94C2×#333—111no—
95#1292—111no—
96C23×C11C22⋊Q811yescharacteristic
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11#12111yescharacteristic
101C2×C4×C11#12111yescharacteristic
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11C22⋊Q811yescharacteristic
104C2×C4×C11C22⋊Q811yescharacteristic
105C2×C4×C11#12611yescharacteristic
106C2×C4×C11C2×SD1611yescharacteristic
107C2×C4×C11#13511yescharacteristic
108C2×C4×C11#13711yescharacteristic
109C2×C4×C11#13711yescharacteristic
110C2×Dic11—42no—
111C2×Dic11—82no—
112Dic22—82no—
113Dic22—82no—
114C8×C11—42no—
115C8×C11—41no—
116C8×C11—41no—
117C8×C11—81no—
118C11⋊C8—22no—
119C11⋊C8—41no—
120C11⋊C8—81no—
121C11⋊C8—81no—
122C2×C4⋊Q8—111no—
123#431C2×D1111yescharacteristic
124C2×#108—221no—
125#423—111no—
126#423C2×D1111yescharacteristic
127C2×C4⋊C8—111no—
128C2×C4⋊C8C2×D1111yescharacteristic
129C4×M16—111no—
130#343—221no—
131#343—221no—
132#341—221no—
133#335—221no—
134#334—22no—
135#334—221no—
136#333—221no—
137#333—221no—
138#333—222no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11#39611yescharacteristic
142C22×C11#47511yescharacteristic
143C22×C11#47911yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11#46111yescharacteristic
148C4×C11#46411yescharacteristic
149C4×C11#46511yescharacteristic
150C4×C11#47011yescharacteristic
151C4×C11#47111yescharacteristic
152C4×C11#47311yescharacteristic
153Dic11—82no—
154C22×Q8—112no—
155C2×M16—21no—
156C2×M16—111no—
157C2×M16—111no—
158C2×M16—221no—
159C22×C8—21no—
160C22×C8—221no—
161C4⋊Q8—221no—
162C4⋊Q8—221no—
163C4⋊Q8—221no—
164C4⋊Q8—221no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4—221no—
167C2×C42C22×D1111yescharacteristic
168#108—442no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—221no—
173C4⋊C8—221no—
174C4⋊C8—221no—
175C4⋊C8—221no—
176C4⋊C8D4411yescharacteristic
177C4⋊C8D4411yescharacteristic
178C4⋊C8C22⋊D1112yes—
179C22⋊C8—21no—
180#97—221no—
181C4×C8—21no—
182C4×C8—221no—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11#206411yescharacteristic
186C2×C11#206611yescharacteristic
187C2×C11#206911yescharacteristic
188C2×Q8—222no—
189C2×Q8—222no—
190C2×Q8—882no—
191C22×C4—222no—
192C22×C4#433911yescharacteristic
193C22×C4D4×D1111yescharacteristic
194C22×C4Q8×D1111yescharacteristic
195M16—41no—
196M16—41no—
197M16—112no—
198M16—221no—
199M16—221no—
200M16—221no—
201M16—441no—
202M16—441no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—22no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—221no—
210C2×C8—221no—
211C2×C8—441no—
212C2×C8—441no—
213C2×C8—881no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C42C2×D4411yescharacteristic
219C42#434111yescharacteristic
220C42#434311yescharacteristic
221C42C2×C22⋊D1111yescharacteristic
222C11#1060911yescharacteristic, complemented, Sylow
223C23#6694911yescharacteristic
224Q8—882no—
225Q8—882no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—442no—
230C2×C4—882no—
231C2×C4#6694811yescharacteristic
232C2×C4#6695011yescharacteristic
233C2×C4#6695111yescharacteristic
234C2×C4SD16×D1111yescharacteristic
235C2×C4#6696811yescharacteristic
236C2×C4#6696811yescharacteristic
237C2×C4#6696911yescharacteristic
238C2×C4#6698311yescharacteristic
239C2×C4#6699211yescharacteristic
240C2×C4#6699911yescharacteristic
241C8—41no—
242C8—41no—
243C8—42no—
244C8—81no—
245C8—222no—
246C8—441no—
247C8—881no—
248C8—881no—
249C22—21no—
250C22—21no—
251C22#1062246711yescharacteristic
252C22#1062247011yescharacteristic
253C22#1062260711yescharacteristic
254C4—21no—
255C4—21no—
256C4—21no—
257C4—882no—
258C4#1062247711yescharacteristic
259C4#1062248111yescharacteristic
260C4#1062275411yescharacteristic
261C4#1062275611yescharacteristic
262C4#1062277511yescharacteristic
263C4#1062277911yescharacteristic
264C2—21no—
265C2—21no—
266C2#1306998211yescharacteristic
267C2#1306999211yescharacteristic
268C2#1307001311yescharacteristic
subgroupG/H
centerC22#10622607
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1570C2
socleC22×C11#396
prime radicalC23×C11C22⋊Q8
hypercenter#1570D11
hypocenterC11#10609
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
222. C11#10609semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130696042
#130693922
#130673692
#130672962
C2×#106221192
#130664902
C11×#15702
#1060911